Question

a local employer asked for help selecting a new type of desk chair. thirty employees volunteered, and each employee used the new desk chair for two weeks and the current desk chair for two weeks. to determine which chair was used first, a coin was flipped for each employee. heads represented using the new chair first, and tails represented using the current chair first. at the end of each two - week period, the employees were asked to rate their satisfaction with the new chair. which of the following best describes this study?
a it is not a well - designed experiment because employees were allowed to volunteer instead of being randomly selected.
b it is not a well - designed experiment because only one new chair was used. at least two new treatments must be used.
c it is not a well - designed experiment because each employee was assigned both treatments, and each employee should be assigned only one.
d it is not a well - designed experiment because using a coin flip does not guarantee that fifteen employees will use each chair first.
e it is a well - designed experiment because there is random assignment, replication, and comparison of at least two treatment groups.

Explanation:

• Option A: Volunteer selection does not necessarily make an experiment not well - designed. The key is random assignment within the experiment, not random selection of participants in some cases (especially when it's about comparing two treatments on the same set of subjects in a proper way).
• Option B: The goal is to compare the new chair with the current one. Using only one new chair (the one being tested) is fine for this comparison. We don't need multiple new treatments as the "treatment" is the new chair versus the old one.
• Option C: Having each employee use both chairs (with random assignment of the order) is a valid experimental design (a matched - pairs design in a sense). It can control for individual differences among employees.
• Option D: A coin flip is a random assignment method. In probability, as the number of trials (here, \(n = 30\) coin flips) increases, the proportion of heads and tails gets closer to \(0.5\). But even if it's not exactly \(15\) heads and \(15\) tails, random assignment still helps in reducing bias. The fact that it's random is more important than the exact equal split in the short - run (for \(n=30\)).
• Option E:
• Random assignment: The coin flip is a form of random assignment (to decide the order of using the chairs). This helps in reducing order - related bias (e.g., if all used the new chair first, they might be more lenient or more critical just because of the order).
• Replication: There are \(n = 30\) employees. Each chair is tested on \(n = 30\) employees (in a sense, each chair has \(n=30\) "observations" considering the order).
• Comparison: There are two "treatments" (using the new chair and using the current chair) that are being compared.

Answer:

E. It is a well - designed experiment because there is random assignment, replication, and comparison of at least two treatment groups.